Design a rectangilar hollow metal waveguide to operate in the X-band such that at an operating free-space wavelength of 3.2 cm
(a) The guide-wavelength for the $$T{E_{{{10}^ - }}}$$ mode is 40% more than the operating free-space wavelength.
(b) The cut-off wavelength for the $$T{M_{{{11}^ - }}}$$ mode is 40% of the cut-off wavelength for the $$T{E_{{{10}^ - }}}$$ mode.

Two vertically oriented half wave dipoles are spaced 1.5 wavelengths apart to from an array. Calculate the half power beam widths of the major lobes of the array, in the horizontal plane for the following two cases when the dipoles are fed with

(a) equal and in - phase currents (Broadside array)
(b) equal currents but with a phase difference of 540⁰ between the two currents (End fire array)

In the case of ground wave propagation, at far-off distances from the transmitting tower antenna, the Poynting vector is

The electric field strength at a far-off point P due to a point charge + q, located at the origin O is 100 millivolts/metre. The point charge is now enclosed by a perfectly conducting hollow metal sphere with its centre at the origin O. The electric field strength at the point, P,